Finite Group Databasebeta

← #18085489

Subgroups — #18085489

Order 4864.

574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574459C211yesmaximal, characteristic
2#14568120C211yesmaximal, characteristic
3#14568113C211yesmaximal, characteristic
4#14563713C211yesmaximal, characteristic
5#14562154C211yesmaximal, characteristic
6#14562154C211yesmaximal, characteristic
7C19×#1297C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×#10597370C2211yescharacteristic
10C22×C4⋊Dic19C2211yescharacteristic
11#11926875—21no—
12#11926875—21no—
13#11926802—22no—
14#11926702—21no—
15#11926702—21no—
16#11926508C2211yescharacteristic
17#11926484—22no—
18#11926476—22no—
19#11926450—21no—
20#11926450—21no—
21#11926419—22no—
22#11926414—21no—
23#11926410—21no—
24#11926405—22no—
25#11926312—22no—
26#11926280—22no—
27#11926280—22no—
28C19×#407C2211yescharacteristic
29C4×C22⋊C4×C19C2211yescharacteristic
30C4×C22⋊C4×C19C2211yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C23×Dic19D412yes—
33C22×Dic38D411yescharacteristic
34C22×Dic38D411yescharacteristic
35C2×M16×C19D412yes—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C42×C19—21no—
39C2×C42×C19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—24no—
49C2×C4⋊Dic19D411yescharacteristic
50C2×C4⋊Dic19D411yescharacteristic
51#10597370—21no—
52#10597370—21no—
53#10597370—21no—
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59C2×Dic19⋊C4—21no—
60C2×Dic19⋊C4—21no—
61C2×#64520—21no—
62C2×Dic76—22no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×#95D412yes—
66C19×#95D412yes—
67C19⋊#95—24no—
68C19⋊#95—24no—
69C19⋊#95—24no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72#10597274—22no—
73#10597273—22no—
74#10597273—22no—
75C24×C19C2×D411yescharacteristic
76C22×C4×C19—22no—
77C22×C4×C19—22no—
78C22×C4×C19—42no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—22no—
90C22×Dic19—22no—
91C22×Dic19—22no—
92C22×Dic19—44no—
93C2×Dic38—21no—
94C2×Dic38—21no—
95C2×Dic38—21no—
96C2×Dic38—21no—
97C2×Dic38—42no—
98C2×Dic38—42no—
99M16×C19—42no—
100C2×C8×C19—22no—
101C22⋊C4×C19—24no—
102C22⋊C4×C19—42no—
103C42×C19—42no—
104C42×C19—42no—
105C22⋊Dic19—41no—
106C22⋊Dic19—41no—
107C22⋊Dic19—41no—
108C22⋊Dic19—41no—
109C4⋊Dic19—21no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—41no—
114C4⋊Dic19—41no—
115C4⋊Dic19—41no—
116C4⋊Dic19—41no—
117C4⋊Dic19—84no—
118Dic19⋊C4—41no—
119Dic19⋊C4—41no—
120Dic19⋊C4—41no—
121Dic19⋊C4—41no—
122#64520—42no—
123C2×C19⋊C8—41no—
124Dic76—82no—
125#10335—191nomaximal, Sylow
126C23×C19—22no—
127C23×C19—22no—
128C23×C19—41no—
129C23×C19#12011yescharacteristic
130C23×C19#12011yescharacteristic
131C23×C19#12111yescharacteristic
132C2×C4×C19—22no—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—24no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19#12011yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19#12711yescharacteristic
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—44no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—44no—
158C2×Dic19—42no—
159C2×Dic19—82no—
160Dic38—42no—
161Dic38—42no—
162Dic38—81no—
163Dic38—81no—
164C8×C19—42no—
165C19⋊C8—81no—
166#3195—191no—
167#2503—191no—
168#2502—191no—
169#1821—191no—
170#1508—191no—
171#1508—191no—
172#1297D1911yescharacteristic
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—44no—
181C22×C19#39211yescharacteristic
182C22×C19#45512yes—
183C22×C19#45612yes—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—44no—
188C4×C19—82no—
189C4×C19#45812yes—
190Dic19—81no—
191Dic19—82no—
192Dic19—81no—
193Dic19—81no—
194Dic19—81no—
195C2×C22⋊Q8—191no—
196C2×C22⋊Q8—191no—
197C22×C4⋊C4—191no—
198#483—381no—
199#483—381no—
200#470—382no—
201#451—381no—
202#451—381no—
203#407—191no—
204#407C2×D1911yescharacteristic
205#400—382no—
206#398—382no—
207#391—381no—
208#391—381no—
209#385—382no—
210#384—381no—
211#382—381no—
212#381—382no—
213C4×C22⋊C4C2×D1911yescharacteristic
214C4×C22⋊C4C2×D1911yescharacteristic
215#343—382no—
216#328—382no—
217#328—382no—
218C2×C19—22no—
219C2×C19—22no—
220C2×C19—41no—
221C2×C19#200411yescharacteristic
222C2×C19#200511yescharacteristic
223C2×C19#202211yescharacteristic
224C22×Q8—191no—
225C22×Q8—191no—
226C23×C4—192no—
227C23×C4C22×D1911yescharacteristic
228C2×Q16—382no—
229C2×M16—381no—
230C2×M16D7612yes—
231C22⋊Q8—381no—
232C22⋊Q8—381no—
233C22⋊Q8—381no—
234C22⋊Q8—381no—
235C22⋊Q8—381no—
236C22⋊Q8—381no—
237C22⋊Q8—381no—
238C22⋊Q8—381no—
239C2×C4⋊C4—191no—
240C2×C4⋊C4—191no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4—384no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C42—21no—
255C2×C42—21no—
256#106—382no—
257#103—382no—
258#103—382no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—381no—
262C22⋊C8—381no—
263#95—384no—
264#95—384no—
265#95—384no—
266#95D7612yes—
267#95D7612yes—
268C19#1033511yescharacteristic, complemented, Sylow
269C24D4×D1911yescharacteristic
270C2×Q8—381no—
271C2×Q8—381no—
272C2×Q8—381no—
273C2×Q8—381no—
274C2×Q8—762no—
275C2×Q8—762no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—382no—
283C22×C4—382no—
284C22×C4—381no—
285C22×C4—382no—
286C22×C4—764no—
287C22×C4C2×D7611yescharacteristic
288C22×C4C2×D7611yescharacteristic
289C22×C4C2×D7611yescharacteristic
290C22×C4D4×D1911yescharacteristic
291C22×C4D4×D1911yescharacteristic
292C22×C4#6454511yescharacteristic
293Q16—1522no—
294M16—42no—
295M16—762no—
296C2×C8—22no—
297C2×C8—761no—
298C4⋊C4—381no—
299C4⋊C4—381no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C4⋊C4—761no—
303C4⋊C4—761no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C4⋊C4—761no—
307C4⋊C4—761no—
308C4⋊C4—761no—
309C4⋊C4—761no—
310C4⋊C4—1524no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—761no—
314C22⋊C4—761no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C42—42no—
318C42—42no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#1059732811yescharacteristic
323C23#1059732811yescharacteristic
324C23#1059734111yescharacteristic
325Q8—762no—
326Q8—762no—
327Q8—1521no—
328Q8—1521no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—764no—
342C2×C4—762no—
343C2×C4—762no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—762no—
349C2×C4—762no—
350C2×C4—764no—
351C2×C4—762no—
352C2×C4—1522no—
353C2×C4#1059732011yescharacteristic
354C2×C4#1059732811yescharacteristic
355C2×C4#1059734111yescharacteristic
356C2×C4#1059734111yescharacteristic
357C8—42no—
358C8—1521no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22#1192645411yescharacteristic
368C22#1192672312yes—
369C22#1192672812yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—82no—
375C4—1522no—
376C4—1521no—
377C4—1521no—
378C4—1521no—
379C4—1521no—
380C4#1192673512yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1456466711yescharacteristic
385C2#1456467411yescharacteristic
386C2#1456476711yescharacteristic
subgroupG/H
centerC22#11926454
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1297D19
hypocenterC19#10335
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
268. C19#10335semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145744592
#145681202
#145681132
#145637132
#145621542
C19×#12972
#1033519